The Kindle Personal Documents Service will allow you to sync non-Amazon books between a Kindle and the iPad/iPhone/iPod Kindle apps. I expect that Amazon will expand this to include other Kindle apps.

Is this available outside the U.S.? The OP is in Japan. I see you're in Canada, but generally we don't have access to the Kindle Personal Documents Service unless we jump through some hoops to hide the fact we're not in the U.S. (Which I tried to do following instructions others have offered here and couldn't get it to work. And frankly, it's too much of a bother to worry about.)